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

Author

Johannes W. Meijer, Sep 21 2010

Keywords

• easy
• nonn

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).

Crossrefs

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

Cf. A013609, A180662.

Programs

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

Magma

R:=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

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 *)

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

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

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).