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 A273373 Squares ending in digit 6. 5
 16, 36, 196, 256, 576, 676, 1156, 1296, 1936, 2116, 2916, 3136, 4096, 4356, 5476, 5776, 7056, 7396, 8836, 9216, 10816, 11236, 12996, 13456, 15376, 15876, 17956, 18496, 20736, 21316, 23716, 24336, 26896, 27556, 30276, 30976, 33856, 34596, 37636, 38416, 41616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These are the only squares whose second last digit is odd. This implies that the only squares whose last two digits are the same are those ending with 0 or 4; those ending with 1, 5, and 9 are paired with even second last digits. - Waldemar Puszkarz, May 24 2016 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA G.f.: 4*x*(4 + 5*x + 32*x^2 + 5*x^3 + 4*x^4)/((1 + x)^2*(1 - x)^3). a(n) = 4*A047221(n)^2 = (10*n - 3*(-1)^n - 5)^2/4. a(n) = A090773(n)^2. - Michel Marcus, May 25 2016 Sum_{n>=1} 1/a(n) = 2*Pi^2/(25*(5+sqrt(5))). - Amiram Eldar, Feb 16 2023 MAPLE seq(seq((10*i+j)^2, j=[4, 6]), i=0..20); # Robert Israel, May 24 2016 MATHEMATICA Table[(10 n - 3 (-1)^n - 5)^2/4, {n, 1, 50}] CoefficientList[Series[4 (4 + 5 x + 32 x^2 + 5 x^3 + 4 x^4) / ((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] Select[Range[250]^2, Mod[#, 10]==6&] (* Harvey P. Dale, May 31 2020 *) PROG (Magma) /* By definition: */ [n^2: n in [0..200] | Modexp(n, 2, 10) eq 6]; (Magma) [(10*n - 3*(-1)^n - 5)^2/4: n in [1..50]]; CROSSREFS Cf. A000290, A047221, A090773. Cf. A017341 (numbers ending in 6), A017343 (cubes ending in 6). Cf. squares with last digit k: A017270 (k=0), A273372 (k=1), A273375 (k=4), A017330 (k=5), this sequence (k=6), A273374 (k=9). Sequence in context: A076956 A075369 A318425 * A264546 A218523 A300535 Adjacent sequences: A273370 A273371 A273372 * A273374 A273375 A273376 KEYWORD nonn,base,easy AUTHOR Vincenzo Librandi, May 21 2016 EXTENSIONS Corrected and extended by Bruno Berselli, May 23 2016 STATUS approved

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Last modified August 3 02:19 EDT 2024. Contains 374875 sequences. (Running on oeis4.)