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

Author

Amarnath Murthy, Nov 01 2002

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A077168, A077170.

Programs

Mathematica

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

PARI

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

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

Extensions

More terms from Sascha Kurz, Feb 10 2003