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Search: id:A105968
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| A105968 |
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a(n) = 4*a(n-1) - a(n-2) - 2*(-1)^n, a(0) = 1, a(1) = 4. |
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2
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| 1, 4, 13, 50, 185, 692, 2581, 9634, 35953, 134180, 500765, 1868882, 6974761, 26030164, 97145893, 362553410, 1353067745, 5049717572, 18845802541, 70333492594, 262488167833, 979619178740, 3655988547125, 13644335009762
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This sequence is the (type 1A) "jbasejfor" transformation of the sequence (-1, -1, -1, -1, ..) with respect to the floretion given in the program code. Under the same conditions, the jbasejfor transformation of the sequence (1, 1, 1, 1, ...) is A006253 [Number of perfect matchings (or domino tilings) in C_4 X P_n]; the jbasejfor transformation of the sequence (1, -1, 1, -1, ...) is A001075 [Chebyshev's T(n,x) polynomials evaluated at x=2]; the jbasejfor transformation of the sequence (-1, 1, -1, 1, ...) is A001353 [3*a(n)^2 + 1 is a perfect square]. In this sense, the sequences (a(n)), A006253, A001075 and A001353 form a "quartett".
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FORMULA
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G.f. (2*x+1)*(1-x)/((x+1)*(x^2-4*x+1)). a(n) + a(n+1) = A054491(n+1) - A054491(n)
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: 4jbasejforseq[ + .25'i + .25'j + .25'k + .25i' + .25j' + .25k' + .25'ii' + .25'jj' + .25'kk' + .25'ij' + .25'ik' + .25'ji' + .25'jk' + .25'ki' + .25'kj' + .25e]. ForType: 1A. 1vesforseq = (-1, -1, -1, -1, ..).
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CROSSREFS
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Cf. A006253, A001075, A001353, A054491.
Sequence in context: A101125 A056275 A149455 this_sequence A149456 A149457 A149458
Adjacent sequences: A105965 A105966 A105967 this_sequence A105969 A105970 A105971
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KEYWORD
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easy,nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Apr 28 2005
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