A298025 Partial sums of A298024.

1, 5, 15, 29, 47, 71, 99, 131, 169, 211, 257, 309, 365, 425, 491, 561, 635, 715, 799, 887, 981, 1079, 1181, 1289, 1401, 1517, 1639, 1765, 1895, 2031, 2171, 2315, 2465, 2619, 2777, 2941, 3109, 3281, 3459, 3641, 3827, 4019, 4215, 4415, 4621, 4831, 5045, 5265, 5489, 5717

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A298024. - Ray Chandler, Aug 31 2023

Links

Rémy Sigrist, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Formula

From Colin Barker, Jan 21 2018: (Start)

G.f.: (1 + 3*x + 6*x^2 + 3*x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4. (End)

a(n) = 7/3*n^2 + 7/3*n + O(1). - Charles R Greathouse IV, May 31 2026

Mathematica

LinearRecurrence[{2, -1, 1, -2, 1}, {1, 5, 15, 29, 47}, 50] (* Paolo Xausa, Feb 24 2026 *)

Prog

(PARI) a(n)=(7*n^2+7*n+55\4^(n%3)%4)/3 \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Cf. A298024.

Sequence in context: A382311 A129393 A268581 * A162525 A212871 A188350

Adjacent sequences: A298022 A298023 A298024 * A298026 A298027 A298028

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 21 2018

Extensions

More terms from Rémy Sigrist, Jan 21 2018

Status

approved