A101032 Table (read by rows) giving the coefficients of sum formulas of n-th Lucas numbers (A000204). The k-th row (k>=1) contains T(i,k) for i=1 to k, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies L(n) = Sum_{i=1..k} T(i,k) * n^(k-i) / (k-1)!.

1, 1, 1, 1, -1, 2, 1, -6, 17, 6, 1, -14, 83, -142, 24, 1, -25, 265, -1235, 2314, 120, 1, -39, 655, -5565, 24184, -41556, 720, 1, -56, 1372, -18200, 137599, -556304, 944628, 5040, 1, -76, 2562, -48664, 560049, -3884524, 15021068, -24875376, 40320, 1, -99, 4398, -113022, 1829793, -19043451

Offset

1,6

Links

Table of n, a(n) for n=1..51.

Ron Knott, The Lucas Numbers in Pascal's Triangle.

Example

L(13)=521; substituting n=13 in the formula of the k-th row we obtain k=7 and the coefficients
T(i,7) will be the following: 1,-39,655,-5565,24184,-41556,720,
=> L(13) = [13^6-39*13^5+655*13^4-5565*13^3+24184*13^2-41556*13+720]/6! = 521.

Crossrefs

Cf. A101033, A000204, A100492, A099731, A000045, A094216, A094638, A000108.

Sequence in context: A049951 A025263 A097947 * A366356 A365109 A025271

Adjacent sequences: A101029 A101030 A101031 * A101033 A101034 A101035

Keyword

sign,tabl

Author

André F. Labossière, Nov 30 2004

Status

approved