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
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).
Programs
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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