

A104563


A floretiongenerated 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
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OFFSET

0,3


LINKS

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


FORMULA

G.f. (x(x^3+1))/((x^2+1)(1x)^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.(1x)/(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



