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0, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1215, 1265, 1316, 1368, 1421, 1475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=A000096 + 3 * A001477, a(n)=A055999 + A001477 and a(n)=A056115 - A001477 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 01 2006
a(n) = A126890(n,4) for n>3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 193.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.(x)=x(5-4x)/(1-x)^3.
a(n)=C(n,2)-4*n,n>=9 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006
Equals A028569/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = -f(n,n-1,5), for n>=1. [From Milan R. Janjic (agnus(AT)blic.net), Dec 20 2008]
a(n)=n+a(n-1)+4. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
a(n)= sum((k+4)!/(k+3)!,k=1..n) [From Gary Detlefs (gdetlefs(AT)aol.com), Aug 10 2010]
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MATHEMATICA
| lst={}; Do[AppendTo[lst, n*(n+9)/2], {n, 0, 5!}]; lst ...and/or... s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 4, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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CROSSREFS
| Equals A000217(n+4)-10. Cf. A000096, A055998 and A055999.
Column m=2 of (1, 5)-Pascal triangle A096940.
Cf. A000096, A055998, A001477.
Cf. numbers of the form n*(d*n+10-d)/2 indexed in A140090.
Sequence in context: A145005 A004083 A190365 * A080566 A094684 A140697
Adjacent sequences: A055997 A055998 A055999 * A056001 A056002 A056003
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jun 16 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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