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A279946 Numbers that are both dodecagonal and centered heptagonal. 1
1, 10396, 326656, 2619897841, 82318050361, 660219495802336, 20744313326831116, 166376633378560463881, 5227608446905776928921, 41927244364003774523222476, 1317367783816405284315203776, 10565749434051302554022550018121, 331979316252074156011094205115681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Jon E. Schoenfield, Dec 24 2016: (Start)

Intersection of dodecagonal numbers A051624 and centered heptagonal numbers A069099. A051624(j) = j(5j - 4), A069099(k) = (7*k^2 - 7^k + 2)/2, and the table below gives indices j and k at which A051624(j) = A069099(k):

.

  n               a(n)         j         k

  =  =================  ========  ========

  1                  1         1      0, 1

  2              10396        46        55

  3             326656       256       306

  4         2619897841     22891     27360

  5        82318050361    128311    153361

  6    660219495802336  11491036  13734415

  7  20744313326831116  64411666  76986666

  ... (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).

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

EXAMPLE

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)

MATHEMATICA

LinearRecurrence[{1, 252002, -252002, -1, 1}, {1, 10396, 326656, 2619897841, 82318050361}, 20] (* Harvey P. Dale, Jul 06 2021 *)

PROG

(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

CROSSREFS

Cf. dodecagonal numbers A051624, centered heptagonal numbers A069099.

Sequence in context: A290035 A289954 A263890 * A031866 A262800 A157445

Adjacent sequences:  A279943 A279944 A279945 * A279947 A279948 A279949

KEYWORD

nonn,easy

AUTHOR

Ann Skoryk, Dec 23 2016

STATUS

approved

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)