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A301693
Partial sums of A301692.
1
1, 5, 12, 21, 33, 49, 70, 95, 121, 150, 184, 222, 263, 305, 351, 403, 458, 515, 573, 636, 706, 778, 851, 925, 1005, 1093, 1182, 1271, 1361, 1458, 1564, 1670, 1775, 1881, 1995, 2119, 2242, 2363, 2485, 2616, 2758, 2898, 3035, 3173, 3321, 3481, 3638, 3791, 3945, 4110, 4288, 4462, 4631, 4801, 4983, 5179, 5370, 5555, 5741, 5940, 6154, 6362, 6563, 6765, 6981, 7213, 7438, 7655, 7873, 8106, 8356, 8598, 8831, 9065, 9315, 9583, 9842, 10091, 10341, 10608, 10894, 11170, 11435, 11701, 11985, 12289, 12582, 12863, 13145, 13446, 13768, 14078, 14375, 14673, 14991, 15331, 15658, 15971, 16285, 16620, 16978
OFFSET
0,2
COMMENTS
Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301692. - Ray Chandler, Aug 30 2023
FORMULA
From Colin Barker, Apr 07 2018: (Start)
G.f.: (1 + x)^2*(1 + x + x^3 + x^4 - x^5)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)^2).
a(n) = a(n-1) + 2*a(n-5) - 2*a(n-6) - a(n-10) + a(n-11) for n>13. (End)
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 2, -2, 0, 0, 0, -1, 1}, {1, 5, 12, 21, 33, 49, 70, 95, 121, 150, 184, 222, 263, 305}, 100] (* Paolo Xausa, Jul 31 2024 *)
CROSSREFS
Cf. A301692.
Sequence in context: A346379 A354399 A256320 * A038794 A225284 A271250
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 25 2018
STATUS
approved