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 A333836 Number of ways to write n as the difference of two positive k-gonal numbers for k >= 3. 3
 0, 1, 2, 2, 4, 2, 5, 3, 6, 3, 6, 4, 7, 4, 7, 5, 8, 4, 7, 5, 10, 6, 7, 5, 10, 5, 10, 5, 9, 7, 9, 6, 11, 6, 10, 6, 12, 5, 11, 7, 11, 6, 9, 7, 13, 9, 9, 8, 12, 7, 13, 7, 9, 7, 11, 9, 17, 7, 7, 8, 13, 6, 14, 9, 17, 8, 11, 6, 12, 9, 11, 9, 13, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Records occur at indices 1, 2, 3, 5, 7, 9, 13, 17, 21, 33, 37, 45, 57, 105, 145, 217, 225, 273, 385, 495, 561, 651, 705, 945, 1105, ... - Peter Kagey, Nov 18 2020 LINKS Peter Kagey, Table of n, a(n) for n = 1..5000 OEIS Wiki, Figurate numbers: Polygonal numbers FORMULA a(n) = A333822(n) - A177025(n) for n > 2. EXAMPLE The a(9) = 6 ways of writing 9 as the difference of two k-gonal numbers are: A000217(4) - A000217(1) = 10 -  1 (triangular), A000217(5) - A000217(3) = 15 -  6 (triangular), A000217(9) - A000217(8) = 45 - 36 (triangular), A000290(5) - A000290(4) = 25 - 16 (square), A000384(3) - A000384(2) = 15 -  6 (hexagonal), and A001107(2) - A001107(1) = 10 -  1 (10-gonal). MATHEMATICA b := 74 CoefficientList[ Series[Sum[    Sum[x^(k*(p*k - (p - 2))/2)*x^(p*k)/(1 - x^(p*k)), {k, 1, b}], {p,     1, b - 1}], {x, 0, b}], x] CROSSREFS Cf. A177025, A333822. Cf. A000217, A000290, A000384, A001107. Sequence in context: A129296 A300837 A321443 * A125296 A294097 A233520 Adjacent sequences:  A333833 A333834 A333835 * A333837 A333838 A333839 KEYWORD nonn AUTHOR Peter Kagey, Apr 07 2020 STATUS approved

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Last modified June 20 00:16 EDT 2021. Contains 345154 sequences. (Running on oeis4.)