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Search: id:A095797
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| A095797 |
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This sequence was submitted without a definition line. |
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+0
1
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| 1, 1, 1, 1, 4, 11, 14, 6, 35, 75, 70, 24, 204, 540, 570, 210, 1524, 3618, 3528, 1224, 9894, 15050, 25524, 9144, 69612, 169932, 168828, 59364, 467736, 165908, 1775208, 417672, 3226524, 7947084, 794468, 2806416, 21924672, 54371568
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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1. (n+1)-th set of 4 terms = leftmost finite differences of sequences generated from 3rd degree polynomials having n-th row coefficients, (given n = 1,2,3...) For example, first row is (1 1 1 1) with a corresponding polynomial x^3 + x^2 + x + 1. (f(x),x = 1,2,3...) = 4, 15, 40, 85, 156...Leftmost term of the sequence = 4, with finite difference rows: 11, 25, 45, 71...; 14, 20, 26, 32...; and 6, 6, 6, 6. Thus leftmost terms of the sequence 4, 15, 40...and the finite difference rows are (4 11 14 6) which is the second 4-term row. 2. The matrix generator is discussed in A028246, while 2nd degree polynomial examples are A091140, A091141 and A091140. The first degree case is A095795.
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FORMULA
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1. By rows of 4 terms, row n = M^(n-1) * [1 1 1 1] where M = the 4 X 4 matrix [1 1 1 1 / 7 3 1 0 / 12 2 0 0 / 6 0 0 0].
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EXAMPLE
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3rd set of 4 terms = (35, 75, 70, 24) since M^2 * [1 1 1 1] = [35 75 70 24].
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CROSSREFS
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Cf. A028246, A091140, A091141, A091142, A095795, A053698.
Sequence in context: A098060 A154040 A066985 this_sequence A091436 A032822 A003250
Adjacent sequences: A095794 A095795 A095796 this_sequence A095798 A095799 A095800
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 06 2004
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