|
Search: id:A095262
|
|
|
| A095262 |
|
A sequence derived from a truncated Pascal's Triangle matrix. |
|
+0
1
|
|
| 2, 21, 137, 735, 3557, 16191, 70877, 302295, 1266437, 5239311, 21481517, 87506055, 354778517, 1433405631, 5776554557, 23235129015, 93327477797, 374471255151, 1501369969997, 6015936563175, 24095119972277, 96474608387871
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The recursive multipliers (9), (-26), (24) are present with changed signs in the characteristic polynomial of M: x^3 - 9x^2 + 26x - 24.
|
|
FORMULA
|
a(n+3) = 9*a(n+2) - 26*a(n+1) + 24*a(n), a(1) = 2, a(2) = 31, a(3) = 137. Let M = the 3 X 3 matrix [2 0 0 / 3 3 0 / 4 6 4] (derived from Pascal's triangle rows by deleting the 1's and filling in with 0's.). Then M^n * [1 0 0] = [2^n 3*A001047(n) 2*A095262(n)].
|
|
EXAMPLE
|
a(5) = 3557 = 9*735 - 26*137 + 24*21. a(4) = 735 since M^4 *[1 0 0] = [2^4 3*A001047(n) 2*A095262(n)] = [16 195 1470]. Then 735 = 1470/2.
|
|
MATHEMATICA
|
a[n_] := (MatrixPower[{{2, 0, 0}, {3, 3, 0}, {4, 6, 4}}, n].{{1}, {0}, {0}})[[3, 1]]/2; Table[ a[n], {n, 22}] (from Robert G. Wilson v Jun 05 2004)
|
|
CROSSREFS
|
Cf. A001047.
Sequence in context: A109789 A136588 A098661 this_sequence A112673 A037749 A037630
Adjacent sequences: A095259 A095260 A095261 this_sequence A095263 A095264 A095265
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), May 31 2004
|
|
EXTENSIONS
|
Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
|
|
|
Search completed in 0.002 seconds
|
