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A217482 Quarter-square tetrahedrals; a(n)= 1/6*(k*(k - 1)*(k - 2)), k = A002620(n). 1
0, 0, 0, 0, 4, 20, 84, 220, 560, 1140, 2300, 4060, 7140, 11480, 18424, 27720, 41664, 59640, 85320, 117480, 161700, 215820, 287980, 374660, 487344, 620620, 790244, 988260, 1235780, 1521520, 1873200, 2275280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Observation: 3/2*a(n) + 2 is a power of 2 to n = 6 (= {2, 2, 2, 2, 8, 32, 128}).

Conjecture: There are no other tetrahedral numbers (Tetra_n = A000292) > 84 such that 3/2*Tetra_n + 2 is a power of 2. This is true to at least 1.41*10^1505 per computer check by Charles R Greathouse IV on Physics Forums (Nov 2010).

LINKS

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).

Physics Forums, A Tetrahedral Counterpart to Ramanujan-Nagell Triangular Numbers?, Nov 2010.

FORMULA

a(n) = (1/6)*floor(n^2/4)*(floor(n^2/4)-1)*(floor(n^2/4)-2).

G.f.: -4*x^4*(x^4+3*x^3+7*x^2+3*x+1)/((x-1)^7*(x+1)^5). [Colin Barker, Oct 11 2012]

PROG

(PARI) a(n)=my(k=floor(n^2/4)); k*(k-1)*(k-2)/6 \\ Charles R Greathouse IV, Oct 05 2012

CROSSREFS

a(2n + 2) = A178208.

Cf. A000292, A002620.

Sequence in context: A320934 A055296 A140532 * A099898 A003489 A167682

Adjacent sequences:  A217479 A217480 A217481 * A217483 A217484 A217485

KEYWORD

nonn,easy

AUTHOR

Raphie Frank, Oct 04 2012

EXTENSIONS

a(24) corrected by Charles R Greathouse IV, Oct 05 2012

STATUS

approved

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Last modified April 22 04:29 EDT 2019. Contains 322329 sequences. (Running on oeis4.)