A027965 T(n, 2*n-3), T given by A027960.

3, 7, 15, 28, 47, 73, 107, 150, 203, 267, 343, 432, 535, 653, 787, 938, 1107, 1295, 1503, 1732, 1983, 2257, 2555, 2878, 3227, 3603, 4007, 4440, 4903, 5397, 5923, 6482, 7075, 7703, 8367, 9068, 9807, 10585, 11403, 12262, 13163, 14107, 15095, 16128, 17207, 18333, 19507, 20730, 22003

Offset

2,1

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n+2) = A074742(n-1) = A008778(n) + 2 = A000297(n-1) + 3.

From Ralf Stephan, Feb 07 2004: (Start)

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

Differences of A027966. (End)

From G. C. Greubel, Jun 30 2019: (Start)

a(n) = (18 - 10*n + 3*n^2 + n^3)/6.

E.g.f.: (-18 - 12*x + (18 - 6*x + 6*x^2 + x^3)*exp(x))/6. (End)

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {3, 7, 15, 28}, 50] (* G. C. Greubel, Jun 30 2019 *)

Prog

(PARI) vector(50, n, n++; (18-10*n+3*n^2+n^3)/6) \\ G. C. Greubel, Jun 30 2019
(Magma) [(18-10*n+3*n^2+n^3)/6: n in [2..50]]; // G. C. Greubel, Jun 30 2019
(Sage) [(18-10*n+3*n^2+n^3)/6 for n in (2..50)] # G. C. Greubel, Jun 30 2019
(GAP) List([2..50], n-> (18-10*n+3*n^2+n^3)/6) # G. C. Greubel, Jun 30 2019

Crossrefs

A column of triangle A027011.

Sequence in context: A103021 A025587 A101498 * A130145 A023552 A293316

Adjacent sequences: A027962 A027963 A027964 * A027966 A027967 A027968

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Terms a(32) onward added by G. C. Greubel, Jun 30 2019

Status

approved