|
Search: id:A094951
|
|
| |
|
| 6, 31, 144, 621, 2538, 9963, 37908, 140697, 511758, 1830519, 6456024, 22497669, 77590386, 265189059, 899198172, 3027619377, 10130328342, 33705582543, 111577100832, 367662044061, 1206427402746, 3943553157531, 12845313733284
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Performing the same operation but using the multiplier [1 0 0] yields [3^n 2*A027471(n+1) A077616(n). Example: M^4 * [1 0 0] = [81 216 324] where 324 = A077616(4) and 216/2 = 108 = A027471(5).
|
|
FORMULA
|
a(n) = A081038(n) + A077616(n) Let M = the 3 X 3 matrix [3 0 0 / 2 3 0 / 1 2 3]; then M^n * [1 1 1] = [3^n A081038(n) a(n)], where a(n) - A081038(n) = A077616(n).
|
|
EXAMPLE
|
a(3) = 144 = 81 + 63 = A081038(3) + A077616(3).
a(4) = 621 = 297 + 324 = A081038(4) + A077616(4).
a(4) = 621 since M^4 * [1 1 1] = [81 297 621] = [3^4 A081038(4), a(4)].
|
|
MATHEMATICA
|
a[n_] := (MatrixPower[{{3, 0, 0}, {2, 3, 0}, {1, 2, 3}}, n].{{1}, {1}, {1}})[[3, 1]]; Table[ a[n], {n, 23}] (from Robert G. Wilson v Jun 05 2004)
|
|
CROSSREFS
|
Cf. A081038, A077616, A027471.
Sequence in context: A079924 A009076 A012714 this_sequence A099621 A056015 A128740
Adjacent sequences: A094948 A094949 A094950 this_sequence A094952 A094953 A094954
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), May 26 2004
|
|
EXTENSIONS
|
Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
|
|
|
Search completed in 0.002 seconds
|
