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.

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A030429 a(n+2) = 7*a(n+1) - 7*a(n) - 9*n; a(n+4) = 9*a(n+3) - 22*a(n+2) + 21*a(n+1) - 7*a(n).

Original entry on oeis.org

1, 2, 7, 26, 115, 596, 3331, 19100, 110329, 638540, 3697405, 21411974, 124001893, 718129334, 4158891979, 24085338398, 139485124807, 807798504728, 4678193659303, 27092766081872, 156902006957821
Offset: 0

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Author

N. J. A. Sloane

Keywords

Comments

Hypothetical numbers of terms in general expressions for Lovelock tensors. Hypothetical extension of sequence A006373 - C. C. Briggs (ccb104(AT)psu.edu)

Links

Crossrefs

Cf. A006373.

Programs

  • Mathematica
    LinearRecurrence[{9,-22,21,-7},{1,2,7,26},30] (* Harvey P. Dale, Oct 12 2015 *)

Formula

Expansion of (1-7*x+11*x^2-14*x^3)/((1-7*x+7*x^2)*(x-1)^2).
a(n) = 2*(23*A030240(n)-133*A030240(n-1)) -9*n -45. - R. J. Mathar, Mar 14 2011

A202551 Triangle T(n,k), read by rows, given by (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Original entry on oeis.org

1, 1, -1, 0, -1, 1, -1, 1, 1, -1, -1, 3, -2, -1, 1, 0, 2, -5, 3, 1, -1, 1, -2, -2, 7, -4, -1, 1, 1, -5, 7, 1, -9, 5, 1, -1, 0, -3, 12, -15, 1, 11, -6, -1, 1, -1, 3, 3, -21, 26, -4, -13, 7, 1, -1
Offset: 0

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Author

Philippe Deléham, Dec 21 2011

Keywords

Comments

Riordan array (1/(1-x+x^2), x*(x-1)/(1-x+x^2)).

Examples

			Triangle begins :
1
1, -1
0, -1, 1
-1, 1, 1, -1
-1, 3, -2, -1, 1
0, 2, -5, 3, 1, -1

Crossrefs

Cf. A129267, A199324

Formula

T(n,k) = T(n-1,k) + T(n-2,k-1) - T(n-1,k-1) - T(n-2,k).
G.f.: 1/(1+(y-1)*x+(1-y)*x^2).
Sum_{k, 0<=k<=n} T(n,k)*x^k = A190873(n+1), A190871(n+1), A057086(n), A057085(n+1), A057084(n), A030240(n), A030192(n), A030191(n), A001787(n+1), A057083(n), A099087(n), A010892(n), A000007(n), (-1)^n*A000045(n+1) for x = -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2 respectively.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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