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Search: id:A104563
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| A104563 |
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A floretion-generated sequence relating to centered square numbers. |
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+0
1
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| 0, 1, 3, 5, 8, 13, 19, 25, 32, 41, 51, 61, 72, 85, 99, 113, 128, 145, 163, 181, 200, 221, 243, 265, 288, 313, 339, 365, 392, 421, 451, 481, 512, 545, 579, 613, 648, 685, 723, 761, 800, 841, 883, 925, 968, 1013, 1059, 1105, 1152, 1201, 1251
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f. (x(x^3+1))/((x^2+1)(1-x)^3) FAMP result: 2a(n) + 2*A004525(n+1) = A104564(n) + a(n+1) Superseeker results: a(2n+1) = A001844(n) = 2n(n+1) + 1 (Centered square numbers); a(n+1) - a(n) = A098180(n) (Odd numbers with two times the odd numbers repeated in order between them); a(n) + a(n+2) = A059100(n+1) = A010000(n+1); a(n+2) - a(n) = A047599(n+1) (Numbers that are congruent to {0, 3, 4, 5} mod 8) a(n+2) - 2a(n+1) + a(n) = A007877(n+3) (Period 4 sequence with initial period (0, 1, 2, 1)) Coefficients of g.f.(1-x)/(1+x) matches A004525 Coefficients of g.f./(1+x) matches A054925
(1/4) [2n^2 + 4 - cos(n*Pi/2) ]. - Ralf Stephan, May 20 2007
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: a(n) = 1vesrokseq[A*B] with A = - .5'i - .5i' + .5'ii' + .5e, B = + .5'ii' - .5'jj' + .5'kk' + .5e. RokType: Y[sqa.Findk()] = Y[sqa.Findk()] + Math.signum(Y[sqa.Findk()])*p (internal program code). Note: many slight variations of the "RokType" already exist- such that it has become difficult to assign them all names.
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CROSSREFS
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Cf. A001844, A004525, A104564, A098180, A059100, A010000, A047599, A007877.
Sequence in context: A123929 A036715 A053651 this_sequence A030762 A023500 A035421
Adjacent sequences: A104560 A104561 A104562 this_sequence A104564 A104565 A104566
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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), Mar 15 2005
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