This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A047520 a(n) = 2*a(n-1) + n^2, a(0) = 0. 11
 0, 1, 6, 21, 58, 141, 318, 685, 1434, 2949, 5998, 12117, 24378, 48925, 98046, 196317, 392890, 786069, 1572462, 3145285, 6290970, 12582381, 25165246, 50331021, 100662618, 201325861, 402652398, 805305525, 1610611834, 3221224509 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Convolution of squares (A000290) and powers of 2 (A000079). - Graeme McRae, Jun 07 2006 Antidiagonal sums of the convolution array A213568. - Clark Kimberling, Jun 18 2012 This is the partial sums of A050488. - J. M. Bergot, Oct 01 2012 From Peter Bala, Nov 29 2012: (Start) This is the case m = 2 of the recurrence a(n) = m*a(n-1) + n^m, m = 1,2,..., with a(0) = 0. The recurrence has the solution a(n) = m^n*sum {i = 1..n} i^m/m^i and has the o.g.f. A(m,x)/((1-m*x)*(1-x)^(m+1)), where A(m,x) denotes the m-th Eulerian polynomial of A008292. For other cases see A000217 (m = 1), A066999 (m = 3) and A067534 (m = 4). (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..3000 Filippo Disanto, Some Statistics on the Hypercubes of Catalan Permutations, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.2. Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2). FORMULA a(n) = 6*2^n - n^2 - 4n - 6 = 6*A000225(n) - A028347(n+2). a(n) = 2^n*sum_{i=1..n} i^2 / 2^i. - Benoit Cloitre, Jan 27 2002 a(0)=0, a(1)=1, a(2)=6, a(3)=21, a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). - Harvey P. Dale, Aug 21 2011 G.f.: (x*(x+1))/((x-1)^3*(2*x-1)). - Harvey P. Dale, Aug 21 2011 a(n) = sum_{k=0..n-1} A000079(n-k) * A000290(k). - Reinhard Zumkeller, Nov 30 2012 MATHEMATICA k=0; lst={}; Do[k=2*k+n^2; AppendTo[lst, k], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 05 2009 *) RecurrenceTable[{a[0]==0, a[n]==2a[n-1]+n^2}, a[n], {n, 30}] (* or *) LinearRecurrence[{5, -9, 7, -2}, {0, 1, 6, 21}, 31] (* Harvey P. Dale, Aug 21 2011 *) f[n_] := 2^n*Sum[i^2/2^i, {i, n}]; Array[f, 30] (* Robert G. Wilson v, Nov 28 2012 *) PROG (MAGMA) [ 6*2^n-n^2-4*n-6: n in [0..30]]; // Vincenzo Librandi, Aug 22 2011 (Haskell) a047520 n = sum \$ zipWith (*)                   (reverse \$ take n \$ tail a000290_list) a000079_list -- Reinhard Zumkeller, Nov 30 2012 CROSSREFS Cf. A000295. A000217, A008292, A066999, A067534. Sequence in context: A056341 A144899 A053809 * A143115 A258142 A066524 Adjacent sequences:  A047517 A047518 A047519 * A047521 A047522 A047523 KEYWORD nonn,easy AUTHOR Henry Bottomley, Jul 04 2000 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.