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A301725 Partial sums of A301724. 1
1, 7, 17, 33, 56, 83, 114, 152, 196, 244, 298, 358, 422, 492, 569, 650, 735, 827, 925, 1027, 1135, 1249, 1367, 1491, 1622, 1757, 1896, 2042, 2194, 2350, 2512, 2680, 2852, 3030, 3215, 3404, 3597, 3797, 4003, 4213, 4429, 4651, 4877, 5109, 5348, 5591, 5838, 6092, 6352 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301724. - Ray Chandler, Aug 30 2023
LINKS
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 06 2018: (Start)
G.f.: (1 + 4*x + 6*x^3 + x^4 + 3*x^5 + x^6 + 6*x^7 + 4*x^9 + x^10) / ((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^10+4x^9+6x^7+x^6+3x^5+x^4+6x^3+4x+1)/ ((x^4+x^3+x^2+x+1)(x^4-x^3+x^2-x+1)(x-1)^2), {x, 0, 100}], x]] (* Harvey P. Dale, May 05 2022 *)
CROSSREFS
Cf. A301724.
Sequence in context: A066436 A128002 A301695 * A278920 A074275 A051411
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 26 2018
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)