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A098156 Interleave n+1 and 2n+1 and take binomial transform. 5
1, 2, 5, 13, 32, 76, 176, 400, 896, 1984, 4352, 9472, 20480, 44032, 94208, 200704, 425984, 901120, 1900544, 3997696, 8388608, 17563648, 36700160, 76546048, 159383552, 331350016, 687865856, 1426063360, 2952790016, 6106906624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A029579.

An elephant sequence, see A175655. For the central square 16 A[5] vectors, with decimal values between 59 and 440, lead to this sequence (without a(1)). For the corner squares these vectors lead to the companion sequence A066373 (with a leading 1 added). - Johannes W. Meijer, Aug 15 2010

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, Pattern Avoiding Linear Extensions of Rectangular Posets, arXiv:1605.06825 [math.CO], 2016.

Colin Defant, Proofs of Conjectures about Pattern-Avoiding Linear Extensions, arXiv:1905.02309 [math.CO], 2019.

Index entries for linear recurrences with constant coefficients, signature (4,-4).

FORMULA

G.f.: (1-2*x+x^2+x^3)/(1-2*x)^2.

a(n) = (2 * 0^n + Sum_{k=0..n} (-1)^(n-k)*k*binomial(n,k) + 2^(n+1) + 3*n*2^(n-1) )/4.

a(n) = Sum_{j=0..n} Sum_{k=0..n} binomial(n, 2*(k-j)).

a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n, 2*j). - Paul Barry, Jan 13 2005

a(n) = 2^(n-3)*(3*n+4) for n>=2. - Philip B. Zhang, May 25 2016

E.g.f.: (2 + x + (2 + 3*x)*exp(2*x))/4. - Ilya Gutkovskiy, May 31 2016

MATHEMATICA

CoefficientList[Series[(1-2x+x^2+x^3)/(1-2x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 21 2013 *)

PROG

(PARI) {a(n) = if(n==0, 1, if(n==1, 2, 2^(n-3)*(3*n+4)))}; \\ G. C. Greubel, May 08 2019

(MAGMA) [1, 2] cat [2^(n-3)*(3*n+4): n in [2..40]]; // G. C. Greubel, May 08 2019

(Sage) [1, 2]+[2^(n-3)*(3*n+4) for n in (2..40)] # G. C. Greubel, May 08 2019

(GAP) Concatenation([1, 2], List([2..40], n-> 2^(n-3)*(3*n+4))) # G. C. Greubel, May 08 2019

CROSSREFS

Sequence in context: A086758 A179257 A116702 * A267862 A098586 A199812

Adjacent sequences:  A098153 A098154 A098155 * A098157 A098158 A098159

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Aug 29 2004

STATUS

approved

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Last modified November 22 03:41 EST 2019. Contains 329387 sequences. (Running on oeis4.)