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Search: id:A069099
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| 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331, 1471, 1618, 1772, 1933, 2101, 2276, 2458, 2647, 2843, 3046, 3256, 3473, 3697, 3928, 4166, 4411, 4663, 4922, 5188, 5461, 5741, 6028, 6322, 6623, 6931, 7246
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equals the triangular numbers convolved with [ 1, 5, 1, 0, 0, 0,...] [From Gary W. Adamson & Alexander Povolotsky (qntmpkt(AT)yahoo.com), May 29 2009]
Except for the first term, a(n)=7*n+a(n-1), (with a(1)=8) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
E. Weisstein, Centered Polygonal Numbers.
Index entries for sequences related to centered polygonal numbers
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FORMULA
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a(n) = (7n^2 - 7n + 2)/2
a(n)= 1 + sum_{k=1..n} 7*k. - Xavier Acloque Oct 26 2003
Binomial transform of [1, 7, 7, 0, 0, 0,...]; Narayana transform (A001263) of [1, 7, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2007
a(n)=7*n+a(n-1)-7 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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EXAMPLE
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a(5) = 71 because 71 = (7*5^2 - 7*5 + 2)/2 = (175 - 35 + 2)/2 = 142/2.
For n=2, a(2)=7*2+1-7=8; n=3, a(3)=7*3+8-7=22; n=4, a(4)=7*4+22-7=43 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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MATHEMATICA
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lst={}; Do[p=(7*n^2-7*n+2)/2; AppendTo[lst, p], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]
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CROSSREFS
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Cf. A000566 (heptagonal numbers).
Cf. A001263.
Sequence in context: A113744 A058508 A134783 this_sequence A145067 A112684 A048489
Adjacent sequences: A069096 A069097 A069098 this_sequence A069100 A069101 A069102
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KEYWORD
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easy,nice,nonn,new
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AUTHOR
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Terrel Trotter, Jr. (ttrotter(AT)telesal.net), Apr 05 2002
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jun 26 2002
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