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A077169
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Initial terms of rows of A077168.
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6
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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
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refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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For n>3, a(n) = (n^2-n+10)/2.
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
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MATHEMATICA
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Join[{1, 2, 4, 7}, Table[(n^2 - n + 10)/2, {n, 4, 50}]] (* G. C. Greubel, Jul 13 2017 *)
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PROG
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(PARI) concat([1, 2, 4, 7], for(n=4, 50, print1((n^2 - n +10)/2, ", "))) \\ G. C. Greubel, Jul 13 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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