This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350437 #26 Jan 11 2022 22:04:55
%S A350437 0,0,1,2,3,7,12,18,31,52,92,158,269,460,786,1350,2317,3969,6798,11643,
%T A350437 19952,34197,58601,100410,172042,294791,505143,865589,1483206,2541480,
%U A350437 4354847,7462119,12786520,21909974,37543133,64330800,110232005,188884671,323657539,554593317
%N A350437 a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A006942).
%C A350437 The integers are displayed as in A006942, where a 7 is depicted by 3 segments. The negative integers are depicted by using 1 segment more for the minus sign.
%C A350437 Since the integer 0 is depicted by 6 segments, in order to avoid considering -0 in the case n = 7, a(7) is obtained by decreasing of a unit the result of the sum A331529(7) + A331529(6) = 12 + 7 = 19, i.e., a(7) = 19 - 1 = 18.
%C A350437 The same sequence is obtained when 7 and 9 are depicted respectively by 4 and 5 segments (A074458).
%H A350437 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,3,3,1).
%H A350437 <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%H A350437 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A350437 a(7) = 18, otherwise a(n) = A331529(n) + A331529(n-1).
%F A350437 G.f.: x^2*(1 + 2*x + 2*x^2 + 4*x^3 + 6*x^4 + 3*x^5 - x^7 - x^8 - 3*x^9 - 3*x^10 - x^11)/(1 - x^2 - x^3 - x^4 - 3*x^5 - 3*x^6 - x^7).
%F A350437 a(n) = a(n-2) + a(n-3) + a(n-4) + 3*a(n-5) + 3*a(n-6) + a(n-7) for n > 13.
%e A350437 a(7) = 18 since -111, -77, -41, -14, -9, -6, 8, 12, 13, 15, 21, 31, 47, 51, 74, 117, 171 and 711 are displayed by 7 segments.
%e A350437 segments.
%e A350437 __ __ __
%e A350437 __ | | | __ | | __ |__| | __ | |__| __ |__|
%e A350437 | | | | | | | | | __|
%e A350437 (-111) (-77) (-41) (-14) (-9)
%e A350437 __ __ __ __ __ __ __
%e A350437 __ |__ |__| | __| | __| | |__ __| | __| |
%e A350437 |__| |__| | |__ | __| | __| |__ | __| |
%e A350437 (-6) (8) (12) (13) (15) (21) (31)
%e A350437 __ __ __ __ __ __
%e A350437 |__| | |__ | | |__| | | | | | | | | |
%e A350437 | | __| | | | | | | | | | | | |
%e A350437 (47) (51) (74) (117) (171) (711)
%t A350437 P[x_]:=x^2+x^3+x^4+3x^5+3x^6+x^7; c[n_]:=Coefficient[Sum[P[x]^k, {k, Max[1, Ceiling[n/7]], Floor[n/2]}], x, n]; b[n_]:=c[n]-c[n-6]; (* A331529 *)
%t A350437 a[n_]:=If[n!=7,b[n]+b[n-1],18]; Array[a,40,0]
%Y A350437 Cf. A006942, A074458, A331529.
%K A350437 nonn,base,easy
%O A350437 0,4
%A A350437 _Stefano Spezia_, Dec 31 2021