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A080856
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Generalized polygonal numbers.
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22
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1, 5, 25, 61, 113, 181, 265, 365, 481, 613, 761, 925, 1105, 1301, 1513, 1741, 1985, 2245, 2521, 2813, 3121, 3445, 3785, 4141, 4513, 4901, 5305, 5725, 6161, 6613, 7081, 7565, 8065, 8581, 9113, 9661, 10225, 10805, 11401, 12013, 12641, 13285, 13945
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row T(4,n) of A080853
{a(k): 0 <= k < 3} = divisors of 25. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=4, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=3, a(n-1)= coeff(charpoly(A,x),x^(n-2)). [From Milan R. Janjic (agnus(AT)blic.net), Jan 27 2010]
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LINKS
| R. Zumkeller, Enumerations of Divisors [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
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FORMULA
| a(n)=8n^2-4n+1 = (16n^2-8n+2)/2 G.f.: (1+2x+13x^2)/(1-x)^3
a(n)=A060820(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 18 2008]
a(n) = C(n,0) + 4*C(n,1) + 16*C(n,2). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
a(n)=16*n+a(n-1)-12 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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EXAMPLE
| a(1)=16*1+1-12=5; a(2)=16*2+5-12=25; a(3)=16*3+25-12=61 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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CROSSREFS
| A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, A161711, A161712, A161713, A161715, A006261. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 17 2009]
Sequence in context: A146649 A146412 A152734 * A060820 A146404 A179131
Adjacent sequences: A080853 A080854 A080855 * A080857 A080858 A080859
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 23 2003
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