1,1

For sums of two positive octagonal numbers, see: A136345. This is to octagonal numbers A000567 as A089982 is to triangular numbers A000217, and as A009000 is to squares A000290, and as A136117 are to pentagonal numbers A000326), and as A133215 is to hexagonal numbers A000384, and as A117104 is to heptagonal numbers A000566. If Oc(a) + Oc(b) = Oc(c) then a(3a-2) + b(3b+2) = c(3c+2), so solving the quadrataic equations for c we have (when an integer): c = (2 + SQRT(4 + 36a^2 + 36b^2 - 24a - 24b))/6.

B. D. Swan, Table of n, a(n) for n=0,...,1800

Eric Weisstein's World of Mathematics, Octagonal Number

A000567 INTERSECTION {A000567(i) + A000567(j), i, j > 0}. {i*(3*i-2)} INTERSECTION {i*(3*i-2) + j(3*j-2), i > 0}.

Where Oc(n) = A000567(n) = n-th octagonal number:

a(1) = 560 = Oc(14) = 280 + 280 = Oc(10) + Oc(10).

a(2) = 736 = Oc(16) = 560 + 176 = Oc(14) + Oc(8).

a(3) = 1541 = Oc(23) = 1408 + 133 = Oc(22) + Oc(7).

a(4) = 3201 = Oc(33) = 2465 + 736 = Oc(29) + Oc(16).

a(5) = 5461 = Oc(43) = 2821 + 2640 = Oc(31) + Oc(30).

Cf. A000567, A009000, A089982, A136117, A136345.

easy,more,nonn,new

Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 25 2007

Corrected and edited by B. D. Swan (bdswan(AT)gmail.com), Dec 20 2008