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A180676
The Gi3 sums of the Pell-Jacobsthal triangle A013609.
3
1, 1, 1, 1, 17, 337, 6641, 130865, 2578785, 50816737, 1001378849, 19732860833, 388849631729, 7662550168241, 150995835638929, 2975477077435217, 58633827885912001, 1155420016046016193, 22768348266078953793
OFFSET
0,5
COMMENTS
The a(n+3) represent the Gi3 sums of the Pell-Jacobsthal triangle A013609. See A180662 for information about these giraffe and other chess sums.
FORMULA
a(n) = 20*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with a(0)=1, a(1)=1, a(2)=1 and a(3)=1.
a(n+3) = Sum_{k=0..n} A013609(n+3*k,4*k).
G.f.: (1-19*x-13*x^2-17*x^3)/(1-20*x+6*x^2-4*x^3+x^4).
MAPLE
nmax:=18: a(0):=1: a(1):=1: a(2):=1: a(3):=1: for n from 4 to nmax do a(n) := 20*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) od: seq(a(n), n=0..nmax);
MATHEMATICA
LinearRecurrence[{20, -6, 4, -1}, {1, 1, 1, 1}, 20] (* Harvey P. Dale, Jun 07 2015 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1-19*x-13*x^2-17*x^3)/(1-20*x+6*x^2-4*x^3 +x^4)) \\ G. C. Greubel, Jun 11 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-19*x-13*x^2-17*x^3)/(1-20*x+6*x^2-4*x^3+x^4) )); // G. C. Greubel, Jun 11 2019
(Sage) ((1-19*x-13*x^2-17*x^3)/(1-20*x+6*x^2-4*x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jun 11 2019
(GAP) a:=[1, 1, 1, 1];; for n in [5..30] do a[n]:=20*a[n-1]-6*a[n-2] + 4*a[n-3]-a[n-4]; od; a; # G. C. Greubel, Jun 11 2019
CROSSREFS
Cf. A052942 (Gi1), A008999 (Gi2), this sequence (Gi3), A180677 (Gi4).
Sequence in context: A299706 A318597 A142933 * A136270 A009046 A012112
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Sep 21 2010
STATUS
approved