cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A115187 Row sums of triangle A115154 (called Y(3,1)).

Original entry on oeis.org

1, 5, 39, 346, 3230, 31191, 309175, 3129194, 32211432, 336239668, 3551081432, 37876866618, 407453687104, 4415521127579, 48159808659879, 528270329593474, 5823991858003544, 64497989461609224, 717191431082458804
Offset: 0

Views

Author

Wolfdieter Lang, Feb 23 2006

Keywords

Formula

a(n)= sum(A115154(n,m),m=1..n+1), n>=0.

A115188 Second diagonal (M=2) of triangle A115154 (called Y(3,1)).

Original entry on oeis.org

1, 13, 115, 1036, 9688, 93571, 927523, 9387580, 96634294, 1008719002, 10653244294, 113630599852, 1222361061310, 13246563382735, 144479425979635, 1584810988780420, 17471975574010630, 193493968384827670
Offset: 0

Views

Author

Wolfdieter Lang, Feb 23 2006

Keywords

Examples

			115 = a(2) = A064063(4) - 3* A064063(3) = 190 - 3*25.

Formula

a(n)= A115154(n+1,n+1), n>=0.
Recurrence: a(n)= b(n) - 3*b(n-1), with b(n):= A064063(n+2), n>=0.
G.f.: ((-3+2*x) + 3*(1-3*x)*c(3*x))/(x*(2+x)), with the o.g.f. c(x) of A000108 (Catalan).

A115192 Sixth diagonal (M=6) of triangle A115154 (called Y(3,1)).

Original entry on oeis.org

1, 1093, 22417, 333244, 4380151, 54231244, 649940212, 7643456248, 88872211096, 1026178892443, 11798983030675, 135327222190240, 1550024200441495, 17743256268685240, 203091320580519760, 2325213813771735940
Offset: 0

Views

Author

Wolfdieter Lang, Feb 23 2006

Keywords

Formula

a(n)= A115154(n+5,n+1), n>=0.
G.f.: ((-3+36*x-81*x^2+ 2*x^5) + 3*(1-15*x+54*x^2-27*x^3)*c(3*x))/((2+x)*x^5), with the o.g.f. c(x) of A000108 (Catalan).

A115189 Third diagonal (M=3) of triangle A115154 (called Y(3,1)).

Original entry on oeis.org

1, 40, 466, 4870, 50053, 516256, 5371210, 56422444, 598180570, 6395471992, 68897550064, 747270112390, 8154207352045, 89462667739360, 986322436120690, 10922076949690180, 121428345789834430, 1354895520307913680
Offset: 0

Views

Author

Wolfdieter Lang, Feb 23 2006

Keywords

Examples

			466 = a(2) = A064063(5) - 6*A064063(4) = 1606 - 6*190.

Formula

a(n)= A115154(n+2,n+1), n>=0.
Recurrence: a(n)= b(n) - 6*b(n-1), with b(n):=A064063(n+3), n>=0.
G.f.: ((-3+9*x +2*x^2) + 3*(1-6*x)*c(3*x))/((2+x)*x^2), with the o.g.f. c(x) of A000108 (Catalan).

A115190 Fourth diagonal (M=4) of triangle A115154 (called Y(3,1)).

Original entry on oeis.org

1, 121, 1762, 20989, 235543, 2588641, 28259704, 308277688, 3369314986, 36937817182, 406378312834, 4487124168115, 49722977591155, 552884158181785, 6167643983348920, 69012419067802540, 774413615153430670
Offset: 0

Views

Author

Wolfdieter Lang, Feb 23 2006

Keywords

Examples

			a(0)= 1 = 190 - 9*(25-4); a(2) = 1762 = 14506 - 9*(1606-190).

Formula

a(n)= A115154(n+3,n+1), n>=0.
Recurrence: a(n)= b(n) - 9*(b(n-1)-b(n-2)), with b(n):=A064063(n+4), n>=0.
G.f.: ((-3+18*x+2*x^3) + 3*(1-9*x+9*x^2)*c(3*x))/((2+x)*x^3), with the o.g.f. c(x) of A000108 (Catalan).

A115191 Fifth diagonal (M=5) of triangle A115154 (called Y(3,1)).

Original entry on oeis.org

1, 364, 6379, 85384, 1039873, 12146074, 139010356, 1574773276, 17751401206, 199685662642, 2245313830945, 25260355535020, 284496154963705, 3208676674986850, 36246188218732000, 410128577783927380
Offset: 0

Views

Author

Wolfdieter Lang, Feb 23 2006

Keywords

Examples

			a(0)= 1 = 1606 - 3*(4*190-9*25); a(1) = 364 = 14506 - 3*(4*1606-9*190).

Formula

a(n)= A115154(n+4,n+1), n>=0.
Recurrence: a(n)= b(n) - 3*(4*b(n-1)-9*b(n-2)), with b(n):=A064063(n+5), n>=0.
G.f.: ((-3+27*x-27*x^2+2*x^4) + 3*(1-3*x)*(1-9*x)*c(3*x))/((2+x)*x^4), with the o.g.f. c(x) of A000108 (Catalan).
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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