A077169 Initial terms of rows of A077168.

1, 2, 4, 7, 11, 15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125, 141, 158, 176, 195, 215, 236, 258, 281, 305, 330, 356, 383, 411, 440, 470, 501, 533, 566, 600, 635, 671, 708, 746, 785, 825, 866, 908, 951, 995, 1040, 1086, 1133, 1181, 1230, 1280, 1331, 1383

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

For n>3, a(n) = (n^2-n+10)/2.

From G. C. Greubel, Jul 13 2017: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n >= 7.

G.f.: (1-x+x^2-x^5 + x^6)/(1-x)^3.

E.g.f.: (1/2)*(x^2 + 10)*exp(x) - 4 - 3*x + x^2 - x^3/6. (End)

Sum_{n>=0} 1/a(n) = 1177/840 + 2*Pi*tanh(sqrt(39)*Pi/2)/sqrt(39). - Amiram Eldar, Dec 13 2022

Mathematica

Join[{1, 2, 4, 7}, Table[(n^2 - n + 10)/2, {n, 4, 50}]] (* G. C. Greubel, Jul 13 2017 *)

Prog

(PARI) concat([1, 2, 4, 7], for(n=4, 50, print1((n^2 - n +10)/2, ", "))) \\ G. C. Greubel, Jul 13 2017

Crossrefs

Cf. A077168, A077170.

Sequence in context: A036700 A025719 A025696 * A094277 A263995 A293239

Adjacent sequences: A077166 A077167 A077168 * A077170 A077171 A077172

Keyword

nonn,easy

Author

Amarnath Murthy, Nov 01 2002

Extensions

More terms from Sascha Kurz, Feb 10 2003

Status

approved