A279946 Numbers that are both dodecagonal and centered heptagonal.
1, 10396, 326656, 2619897841, 82318050361, 660219495802336, 20744313326831116, 166376633378560463881, 5227608446905776928921, 41927244364003774523222476, 1317367783816405284315203776, 10565749434051302554022550018121, 331979316252074156011094205115681
Offset: 1
Examples
From _Jon E. Schoenfield_, Dec 24 2016: (Start) 10396 is both the 46th dodecagonal number and the 55th centered heptagonal number: A051624(46) = 46(5*46 - 4) = 10396 and A069099(55) = (7*55^2 - 7*55 + 2)/2 = 10396. A051624(256) = 256(5*256 - 4) = 326656 = (7*306^2 - 7*306 + 2)/2 = A069099(306). (End)
References
- F. Tapson (1999). The Oxford Mathematics Study Dictionary (2nd ed.). Oxford University Press. pp. 88-89.
Links
- Colin Barker, Table of n, a(n) for n = 1..350
- Wikipedia, Polygonal number
- Index entries for linear recurrences with constant coefficients, signature (1,252002,-252002,-1,1).
Programs
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Mathematica
LinearRecurrence[{1,252002,-252002,-1,1},{1,10396,326656,2619897841,82318050361},20] (* Harvey P. Dale, Jul 06 2021 *) -
PARI
Vec(x*(1 + 10395*x + 64258*x^2 + 10395*x^3 + x^4) / ((1 - x)*(1 - 502*x + x^2)*(1 + 502*x + x^2)) + O(x^20)) \\ Colin Barker, Dec 24 2016
Formula
Empirical: a(1)=1, a(2)=10396, a(3)=326656, a(4)=2619897841, a(n) = 252002*a(n-2) - a(n-4) + 85050 for n > 4. - Jon E. Schoenfield, Dec 24 2016
G.f.: x*(1 + 10395*x + 64258*x^2 + 10395*x^3 + x^4) / ((1 - x)*(1 - 502*x + x^2)*(1 + 502*x + x^2)). - Colin Barker, Dec 24 2016
Comments