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A074377
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Odd triangular numbers decremented and halved.
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24
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0, 1, 7, 10, 22, 27, 45, 52, 76, 85, 115, 126, 162, 175, 217, 232, 280, 297, 351, 370, 430, 451, 517, 540, 612, 637, 715, 742, 826, 855, 945, 976, 1072, 1105, 1207, 1242, 1350, 1387, 1501, 1540, 1660, 1701, 1827, 1870, 2002, 2047, 2185, 2232, 2376, 2425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also called generalized 10-gonal numbers. - T. D. Noe (noe(AT)sspectra.com), Apr 21 2006
It appears that this is zero together the partial sums of A165998. - Omar E. Pol, Sep 10 2011
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LINKS
| Neville Holmes, More Gemometric Integer Sequences
Index to sequences with linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
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FORMULA
| (n(n+1)-2)/4 where n(n+1)/2 is odd.
G.f.: x(1+6x+x^2)/((1-x)(1-x^2)^2). - Michael Somos, Mar 04 2003
a(2k) = k(4k+3); a(2k+1) = (2k+1)^2+k. [From Benoit Jubin (benoit_jubin(AT)yahoo.fr), Feb 05 2009]
a(n) = n^2+n-1/4+(-1)^n/4+n*(-1)^n/2. - R. J. Mathar, Oct 08 2011
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MATHEMATICA
| f[n_]:=n(n+3)/4; Select[Table[f[n], {n, 0, 6!}], IntegerQ] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2010]
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PROG
| (PARI) a(n)=(2*n+3-4*(n%2))*(n-n\2)
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CROSSREFS
| Cf. A011848, A014493, A074378.
Cf. A001107 (10-gonal numbers).
Sequence in context: A064210 A097634 A120312 * A117618 A103119 A054224
Adjacent sequences: A074374 A074375 A074376 * A074378 A074379 A074380
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KEYWORD
| easy,nonn
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AUTHOR
| Neville Holmes (neville.holmes(AT)utas.edu.au), Sep 04 2002
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