The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A063376 a(-1) = 1; for n >= 0, a(n) = 2^n + 4^n = 2^n*(1 + 2^n). 61
 1, 2, 6, 20, 72, 272, 1056, 4160, 16512, 65792, 262656, 1049600, 4196352, 16781312, 67117056, 268451840, 1073774592, 4295032832, 17180000256, 68719738880, 274878431232, 1099512676352, 4398048608256, 17592190238720, 70368752566272 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 COMMENTS Counts closed walks of length 2n+2 at a vertex of the cyclic graph on 8 nodes C_8. The count of closed walks of odd length is zero. See the array w(N,L) and triangle a(K,N) given in A199571 for the general case. - Wolfdieter Lang, Nov 08 2011 Number of monic irreducible polynomials of degree 1 in GF(2^n)[x,y]. - Max Alekseyev, Jan 23 2006 a(n) written in base 2: a(-1) = 1, a(0) = 10, a(n) for n >= 1: 110, 10100, 1001000, 100010000, ..., i.e., number 1, (n-1) times 0, number 1, n times 0 (see A163664). a(n) for n >= 0 is duplicate of A161168. a(n) for n >= 0 is a bisection of A005418. - Jaroslav Krizek, Aug 14 2009 With offset 0 = binomial transform of A122983. - Gary W. Adamson, Apr 18 2011 REFERENCES B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121. See Table 4. LINKS Harry J. Smith, Table of n, a(n) for n = -1..200 M. Archibald, A. Blecher, A. Knopfmacher, M. E. Mays, Inversions and Parity in Compositions of Integers, J. Int. Seq., Vol. 23 (2020), Article 20.4.1. Georgia Benkart, Dongho Moon, Walks on Graphs and Their Connections with Tensor Invariants and Centralizer Algebras, arXiv preprint arXiv:1610.07837 [math.RT], 2016-2017. J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of some polygonal systems representing polycyclic conjugated hydrocarbons, J. Molec. Struct. (Theochem), 364 (1996), 1-13. (See Table 11.) S. Capparelli, A. Del Fra, Dyck Paths, Motzkin Paths, and the Binomial Transform, Journal of Integer Sequences, 18 (2015), #15.8.5. B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, 1996 [Annotated scanned copy of pages 118, 119 only]. T. A. Gulliver, Sums of Powers of Integers Divisible by Three, Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 38, 1895 - 1901. D. Suprijanto and Rusliansyah, Observation on Sums of Powers of Integers Divisible by Four, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, 2219 - 2226. Index entries for linear recurrences with constant coefficients, signature (6,-8). FORMULA a(n) = Sum_{k=0..n} if((n-k) mod 4 = 0, binomial(n, 2*k), 0)}. - Paul Barry, Sep 19 2005 a(n) = 4*a(n-1) - 2^n = 6*a(n-1) - 8*a(n-2) = A001576(n) - 1 = 2*A007582(n) = A005418(2*n+2) = A002378(A000079(n)). G.f.: 1/x + (2-6*x)/((1-2*x)*(1-4*x)). a(n) = ceiling(2^n*(2^n + 1)), n >= -1. - Zerinvary Lajos, Jan 07 2008 E.g.f.: exp(2*x)*cosh(x)^2. - Paul D. Hanna, Oct 25 2012 E.g.f.: (1+Q(0))/4, where Q(k) = 1 + 2/( 2^k - 2*x*4^k/( 2*x*2^k + (k+1)/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Dec 16 2013 EXAMPLE a(1)=6 counts six round trips from, say, vertex no 1: 12121, 18181, 12181, 18121, 12321 and 18781. - Wolfdieter Lang, Nov 08 2011 MAPLE seq(ceil(2^n*(2^n + 1)), n=-1..23); # Zerinvary Lajos, Jan 07 2008 MATHEMATICA Table[2^n + 4^n, {n, 0, 25}] PROG (PARI) a(n)={if(n>=0, 2^n*(1 + 2^n), 1)} \\ Harry J. Smith, Aug 20 2009 (PARI) {a(n)=n!*polcoeff((1 + exp(2*x +x*O(x^n)))^2/4, n)} \\ Paul D. Hanna, Oct 25 2012 (MAGMA)  cat [2^n + 4^n : n in [0..30]]; // Wesley Ivan Hurt, Jul 03 2020 CROSSREFS Cf. A000051, A006516, A007582, A034472, A034474, A034491, A052539, A062394, A062395, A062396, A007689, A063376, A063481, A074600 - A074624, A122983. A column of A323850. Essentially the same as A028402. Sequence in context: A192658 A049141 A049129 * A161168 A049139 A071356 Adjacent sequences:  A063373 A063374 A063375 * A063377 A063378 A063379 KEYWORD easy,nonn AUTHOR Henry Bottomley, Jul 14 2001 EXTENSIONS Entry rewritten by N. J. A. Sloane Jan 23 2006 Definition corrected to a(-1) = 1 by Harry J. Smith, Aug 20 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 23 20:03 EDT 2020. Contains 337975 sequences. (Running on oeis4.)