|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|