A145138 Main diagonal of square array A145153.

0, 1, 2, 6, 20, 71, 259, 960, 3597, 13586, 51635, 197223, 756380, 2910707, 11233311, 43460144, 168502849, 654547456, 2546819347, 9924285801, 38723794820, 151278566731, 591628491483, 2316065644414, 9074988880769, 35587925333525, 139666503235814, 548516611541343

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = [x^n] x/((1-x-x^4)*(1-x)^(n-1)).

Maple

a:= n-> coeftayl(x/(1-x-x^4)/(1-x)^(n-1), x=0, n):
seq(a(n), n=0..30);
# second Maple program:
a:= proc(n) option remember; `if`(n<5, n*(n+1)*(n^2-4*n+6)/6,
       a(n-4)+(2*(35*n^3-207*n^2+310*n-78)*a(n-1)-(203*n^3
       -1244*n^2+1891*n-130)*a(n-2)+(2*n-7)*(7*n-19)*n*
       (10*a(n-3)-2*a(n-5)))/((7*n-26)*(n-1)^2))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Aug 18 2019

Mathematica

a[n_] := SeriesCoefficient[x/(1-x-x^4)/(1-x)^(n-1), {x, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 10 2022 *)

Crossrefs

Cf. A145153, A000004, A000012, A001477, A000217, A000292, A145126, A145127, A145128, A145129, A145130, A017898, A003269, A098578, A145131, A145132, A145133, A145134, A145135, A145136, A145137.

Sequence in context: A150127 A151286 A047126 * A000707 A129777 A108600

Adjacent sequences: A145135 A145136 A145137 * A145139 A145140 A145141

Keyword

nonn

Author

Alois P. Heinz, Oct 03 2008

Status

approved