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 A332243 Starhex honeycomb numbers: a(n) = 13 + 60*n + 60*n^2. 2
 13, 133, 373, 733, 1213, 1813, 2533, 3373, 4333, 5413, 6613, 7933, 9373, 10933, 12613, 14413, 16333, 18373, 20533, 22813, 25213, 27733, 30373, 33133, 36013, 39013, 42133, 45373, 48733, 52213, 55813, 59533, 63373, 67333, 71413, 75613, 79933, 84373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 20. LINKS Table of n, a(n) for n=0..37. John Elias, Illustration of Initial Terms Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 12*(5*n*(n + 1) + 1) + 1. From Stefano Spezia, Feb 07 2020: (Start) O.g.f.: (13 + 94*x + 13*x^2)/(1 - x)^3. E.g.f.: exp(x)*(13 + 120*x + 60*x^2). a(n) = 3*a(n-1) - 3*a(n-2) + a(n-2) for n > 2. (End) a(n) = A082369(A001844(n)). - M. F. Hasler, Jun 09 2023 EXAMPLE Example: a(2) = 13 + 60*2 + 60*2^2 = 373. Illustration of initial terms: . 0 . 0 0 0 0 . 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 * * 0 * * 0 0 0 0 . 0 0 0 * * * * * * 0 0 0 . 0 0 0 0 * * 0 * * 0 0 0 0 . 0 * * 0 0 0 0 * * 0 . * * * 0 0 0 * * * . 0 * * 0 0 0 0 * * 0 . 0 0 0 0 * * 0 * * 0 0 0 0 . 0 0 0 * * * * * * 0 0 0 . 0 0 0 0 0 * * 0 * * 0 0 0 0 . 0 * * 0 0 0 0 0 0 0 . * 0 * 0 0 0 . 0 * * 0 0 0 0 0 . 0 0 . . 13 133 MATHEMATICA Array[12 (5 #^2 + 5 # + 1) + 1 &, 38, 0] (* Michael De Vlieger, Feb 07 2020 *) LinearRecurrence[{3, -3, 1}, {13, 133, 373}, 40] (* Harvey P. Dale, Nov 18 2023 *) PROG (PARI) A332243(n)=n*(n+1)*60+13 \\ M. F. Hasler, Jun 09 2023 CROSSREFS Cf. A003154, A003215, A062786. Subsequence of A082369: cf. formula. Sequence in context: A295603 A199144 A198664 * A081042 A329019 A016153 Adjacent sequences: A332240 A332241 A332242 * A332244 A332245 A332246 KEYWORD easy,nonn AUTHOR John Elias, Feb 07 2020 STATUS approved

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Last modified May 22 17:27 EDT 2024. Contains 372758 sequences. (Running on oeis4.)