|
Search: id:A093953
|
|
|
| A093953 |
|
a(n) = rightmost term in M^n * [1,1,1], where M = a 3 X 3 matrix composed of the first 3 rows of A050166 (fill in the matrix with zeros): = [1 0 0 / 1 2 0 / 1 4 5]. |
|
+0
1
|
|
| 1, 10, 63, 344, 1781, 9030, 45403, 227524, 1138641, 5695250, 28480343, 142409904, 712065901, 3560362270, 17801876883, 89009515484
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
A sequence relating to Catalan numbers.
1. a(n)/a(n-1) tends to 5, a Catalan number. E.g. a(6)/a(5) = 45403/9030 = 4.9948... 2. Generally, with M = an N X N matrix composed of rows of A050166 (along with zeros), M^n * [1,1,1...] generates terms [a, b, c, d...] such that sequences of which a,b,c,d...are members converge upon the Catalan numbers: 1, 2, 5, 14, 42, 132...
Companion (M^n)[3,2] = 4*A016127(n), (M^n)[3,3] = 5^n = A000351(n), so a(n) = a(n-1) + 4*A016127(n-1) + 5^(n-1) for n>0 - Lambert Klasen (lambert.klasen(AT)gmx.net), Jan 30 2005
|
|
FORMULA
|
Or simply with M=[1, 0, 0;1, 2, 0;1, 4, 5], a(n)=(M^n)[3, 1], (adds a leading 0 to sequence) - Lambert Klasen (lambert.klasen(AT)gmx.net), Jan 30 2005
|
|
EXAMPLE
|
a(4) = 1781 since M^4 * [1,1,1] = [1, 31, 1781].
|
|
PROGRAM
|
(PARI) M=[1, 0, 0; 1, 2, 0; 1, 4, 5]; for(i=0, 10, print1((M^i)[3, 1], ", ")) (Klasen)
|
|
CROSSREFS
|
Cf. A050166.
Cf. A016127, A000351.
Sequence in context: A055368 A077616 A145885 this_sequence A075755 A046638 A101467
Adjacent sequences: A093950 A093951 A093952 this_sequence A093954 A093955 A093956
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 18 2004
|
|
|
Search completed in 0.002 seconds
|
