A055583 Seventh column of triangle A055252.

1, 10, 58, 256, 955, 3178, 9740, 28064, 77093, 203930, 523262, 1309520, 3209871, 7731642, 18348240, 42989520, 99612345, 228586890, 520090690, 1174401760, 2634019171, 5872021450, 13019115028, 28722588736, 63082326605, 137975818298, 300647704070, 652835021744, 1413044232503

Offset

0,2

Links

Michael De Vlieger, Table of n, a(n) for n = 0..3295

Robert Davis and Greg Simay, Further Combinatorics and Applications of Two-Toned Tilings, arXiv:2001.11089 [math.CO], 2020.

Index entries for linear recurrences with constant coefficients, signature (10,-42,96,-129,102,-44,8).

Formula

G.f.: 1/(((1-2*x)^3)*(1-x)^4).

a(n) = A055252(n+6, 6).

a(n) = Sum_{j=0..n-1} a(j) + A055250(n), n >= 1.

E.g.f.: exp(x)*(96*exp(x)*(7 - 4*x + 2*x^2) - 666 - 234*x - 27*x^2 - x^3)/6. - Stefano Spezia, Apr 07 2026

Mathematica

CoefficientList[Series[1/(((1 - 2 x)^3) (1 - x)^4), {x, 0, 24}], x] (* Michael De Vlieger, Apr 24 2020 *)
LinearRecurrence[{10, -42, 96, -129, 102, -44, 8}, {1, 10, 58, 256, 955, 3178, 9740}, 30] (* Harvey P. Dale, Nov 06 2022 *)

Crossrefs

Cf. A055252, A055249, A055250, partial sums of A055582.

Sequence in context: A189072 A189417 A060157 * A242202 A125320 A321112

Adjacent sequences: A055580 A055581 A055582 * A055584 A055585 A055586

Keyword

easy,nonn

Author

Wolfdieter Lang, May 26 2000

Status

approved