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Search: id:A145069
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| 3, 10, 23, 44, 75, 118, 175, 248, 339, 450, 583, 740, 923, 1134, 1375, 1648, 1955, 2298, 2679, 3100, 3563, 4070, 4623, 5224, 5875, 6578, 7335, 8148, 9019, 9950, 10943, 12000, 13123, 14314, 15575, 16908, 18315, 19798, 21359, 23000, 24723, 26530
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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G.f:: (3-2*x+x^2)/(1-x)^4.
a(n) = sum_{j=2..n+1} A002061(j) for n >= 1.
a(1) = 3; a(n) = a(n-1) + n^2 + n + 1 for n > 1.
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EXAMPLE
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a(2) = a(1) + 2^2 + 2 + 1 = 3 + 4 + 2 + 1 = 10; a(3) = a(2) + 3^2 + 3 + 1 = 10 + 9 + 3 + 1 = 23.
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MATHEMATICA
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lst={}; s=0; Do[s+=n^2+n+1; AppendTo[lst, s], {n, 5!}]; lst
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PROGRAM
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(PARI) {a=0; for(n=1, 42, print1(a=a+n^2+n+1, ", "))}
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CROSSREFS
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Cf. A002061 (n^2 - n + 1), A028387 (n + (n+1)^2), A077415 (zero followed by partial sums of A028387, starting at n=1),
Sequence in context: A041403 A077126 A068043 this_sequence A080204 A115982 A167243
Adjacent sequences: A145066 A145067 A145068 this_sequence A145070 A145071 A145072
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 30 2008
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EXTENSIONS
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Edited. - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 21 2008
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