|
Search: id:A101032
|
|
|
| A101032 |
|
Table (read by rows) giving the coefficients of sum formulae 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)!. |
|
+0
12
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
LINKS
|
R. D. Knott, The Lucas Numbers in Pascal's Triangle.
A. F. Labossiere, Sobalian Coefficients.
A. F. Labossiere, Miscellaneous.
|
|
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.
Adjacent sequences: A101029 A101030 A101031 this_sequence A101033 A101034 A101035
Sequence in context: A049951 A025263 A097947 this_sequence A025271 A100404 A103114
|
|
KEYWORD
|
sign,tabl
|
|
AUTHOR
|
Andre F. Labossiere (boronali(AT)laposte.net), Nov 30 2004
|
|
|
Search completed in 0.002 seconds
|
