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A104563 A floretion-generated sequence relating to centered square numbers. 0
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; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..50.

FORMULA

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

PROG

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.

CROSSREFS

Cf. A001844, A004525, A104564, A098180, A059100, A010000, A047599, A007877.

Sequence in context: A158384 A053651 A175388 * A261175 A265064 A030762

Adjacent sequences:  A104560 A104561 A104562 * A104564 A104565 A104566

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Mar 15 2005

STATUS

approved

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.