A301727 Partial sums of A301726.

1, 6, 17, 33, 54, 81, 114, 152, 195, 244, 298, 357, 422, 492, 567, 648, 735, 827, 924, 1027, 1135, 1248, 1367, 1491, 1620, 1755, 1896, 2042, 2193, 2350, 2512, 2679, 2852, 3030, 3213, 3402, 3597, 3797, 4002, 4213, 4429, 4650, 4877, 5109, 5346, 5589, 5838, 6092, 6351, 6616, 6886, 7161, 7442, 7728, 8019, 8316, 8619, 8927

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301726. - Ray Chandler, Aug 30 2023

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3, -4, 4, -4, 4, -4, 4, -4, 4, -3, 1).

Formula

From Colin Barker, Apr 09 2018: (Start)

G.f.: (1 + x + x^2)*(1 + 2*x + 3*x^4 + 2*x^7 + x^8) / ((1 - x)^3*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).

a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 4*a(n-4) + 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 3*a(n-10) + a(n-11) for n>10.

(End)

Mathematica

Accumulate[CoefficientList[Series[(x^2+x+1)(x^8+2x^7+3x^4+2x+1)/ ((x^4+ x^3+x^2+x+1)(x^4-x^3+x^2-x+1)(x-1)^2), {x, 0, 110}], x]] (* Harvey P. Dale, Sep 25 2020 *)

Crossrefs

Cf. A301726.

Sequence in context: A338894 A237658 A301696 * A038795 A216892 A301711

Adjacent sequences: A301724 A301725 A301726 * A301728 A301729 A301730

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2018

Status

approved