A180677 The Gi4 sums of the Pell-Jacobsthal triangle A013609.

1, 3, 15, 87, 503, 2871, 16311, 92599, 525751, 2985399, 16952759, 96267703, 546663863, 3104271799, 17627835831, 100100959671, 568430652855, 3227875241399, 18329726840247, 104086701305271, 591063984860599

Offset

0,2

Comments

The a(n) represent the Gi4 sums of the Pell-Jacobsthal triangle A013609. See A180662 for information about these giraffe and other chess sums.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-24,32,-16).

Formula

a(n) = 9*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) with a(0)=1, a(1)=3, a(2)= 15 and a(3)= 87.

a(n) = Sum_{k=0..n} A013609(n+3*k,n-k).

G.f.: (1-6*x+12*x^2-8*x^3)/(1-9*x+24*x^2-32*x^3+16*x^4).

Maple

nmax:=21: a(0):=1: a(1):=3: a(2):=15: a(3):=87: for n from 4 to nmax do a(n) := 9*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4) od: seq(a(n), n=0..nmax);

Mathematica

LinearRecurrence[{9, -24, 32, -16}, {1, 3, 15, 87}, 30] (* G. C. Greubel, Jun 11 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1-6*x+12*x^2-8*x^3)/(1-9*x+24*x^2-32*x^3 +16*x^4)) \\ G. C. Greubel, Jun 11 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-6*x+ 12*x^2-8*x^3)/(1-9*x+24*x^2-32*x^3+16*x^4) )); // G. C. Greubel, Jun 11 2019
(Sage) ((1-6*x+12*x^2-8*x^3)/(1-9*x+24*x^2-32*x^3+16*x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jun 11 2019
(GAP) a:=[1, 3, 15, 87];; for n in [5..30] do a[n]:=9*a[n-1]-24*a[n-2] +32*a[n-3]-16*a[n-4]; od; a; # G. C. Greubel, Jun 11 2019

Crossrefs

Cf. A052942 (Gi1), A008999 (Gi2), A180676 (Gi3), this sequence (Gi4).

Cf. A013609, A180662.

Sequence in context: A001931 A306524 A355097 * A220875 A075841 A152596

Adjacent sequences: A180674 A180675 A180676 * A180678 A180679 A180680

Keyword

easy,nonn

Author

Johannes W. Meijer, Sep 21 2010

Status

approved