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A095262
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A sequence derived from a truncated Pascal's Triangle matrix.
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1
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2, 21, 137, 735, 3557, 16191, 70877, 302295, 1266437, 5239311, 21481517, 87506055, 354778517, 1433405631, 5776554557, 23235129015, 93327477797, 374471255151, 1501369969997, 6015936563175, 24095119972277, 96474608387871
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The recursive multipliers (9), (-26), (24) are present with changed signs in the characteristic polynomial of M: x^3 - 9x^2 + 26x - 24.
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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)].
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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.
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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)
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CROSSREFS
| Cf. A001047.
Sequence in context: A136588 A171009 A098661 * A112673 A202028 A037749
Adjacent sequences: A095259 A095260 A095261 * A095263 A095264 A095265
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 31 2004
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EXTENSIONS
| Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
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